ND样本加权回归函数估计的强相合速度

Rate of Strong Consistency of Regression Weighted Function Estimator for Negatively Associated Dependent Samples

设{εi,1≤i≤n}为ND随机误差序列,利用ND序列的Bernstein不等式,在非参数回归模型Yi=g(xi)+εi(1≤i≤n)下,研究未知函数g(x)加权核估计gn(x)=∑n i=1 Yi(xi-xi-1)/hn K((x-xi)/hn)的强相合速度,从而将加权回归函数估计的相合性推广到ND样本.

Let {εi,1≤i≤n} be negatively dependent and random error sequence.With the help of the nonparametric regression model Yi=g（xi）＋εi（1≤i≤n）,we discussed the rate of the strong consistency of the nonparametric regression weighted function estimator gn（x）=∑n i=1Yi（xi-xi-1）/hn K（（x-xi）/hn） for negatively dependent samples using Bernstein inequality.The consistency was extended to the case of negatively dependent samples.